High-order phase transitions in the quadratic family

Abstract

We give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, near the phase transition these functions behave as $x\mapsto \exp (-1/x^2)$ near $x=0$, before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.

arXiv admin note: substantial text overlap with arXiv:1205.1833

References in corpus (2)

• Abundant rich phase transitions in step skew products
• Pesin theory and equilibrium measures on the interval

Cited by in corpus (2)

• Abundant rich phase transitions in step skew products
• Phase Transitions in One-dimensional Translation Invariant Systems: a Ruelle Operator Approach